Solution: The GCF of 138 and 130 is 2
Methods
How to find the GCF of 138 and 130 using Prime Factorization
One way to find the GCF of 138 and 130 is to compare the prime factorization of each number. To find the prime factorization, you can follow the instructions for each number here:
What are the Factors of 138?
What are the Factors of 130?
Here is the prime factorization of 138:
2
1
×
3
1
×
2
3
1
2^1 × 3^1 × 23^1
2 1 × 3 1 × 2 3 1
And this is the prime factorization of 130:
2
1
×
5
1
×
1
3
1
2^1 × 5^1 × 13^1
2 1 × 5 1 × 1 3 1
When you compare the prime factorization of these two numbers, you can see that there are matching prime factors. You can now find the Greatest Common Factor of 138 and 130 by multiplying all the matching prime factors to get a GCF of 138 and 130 as 4:
Thus, the GCF of 138 and 130 is: 4
How to Find the GCF of 138 and 130 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 138 and 130 is to find and list all the factors of each number. Again, you can see how this is done by looking at the “Factors of” articles that are linked to above.
Let’s take a look at the factors for each of these numbers, 138 and 130:
Factors of 138: 1, 2, 3, 6, 23, 46, 69, 138
Factors of 130: 1, 2, 5, 10, 13, 26, 65, 130
When you compare the two lists of factors, you can see that the common factor(s) are 1, 2. Since 2 is the largest of these common factors, the GCF of 138 and 130 would be 2.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 72 and 142?
What is the GCF of 29 and 107?
What is the GCF of 73 and 46?
What is the GCF of 13 and 112?
What is the GCF of 63 and 48?